Persistent homology of unweighted complex networks via discrete Morse theory.

ABSTRACT: Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and undirected networks using persistent homology. Leveraging on the features of discrete Morse theory, our method not only captures the topology of the clique complex of such graphs via the concept of critical simplices, but also achieves close to the theoretical minimum number of critical simplices in several analyzed model and real networks. This leads to a reduced filtration scheme based on the subsequence of the corresponding critical weights, thereby leading to a significant increase in computational efficiency. We have employed our filtration scheme to explore

SUBMITTER: Kannan H 

PROVIDER: S-EPMC6761140 | biostudies-literature | 2019 Sep

REPOSITORIES: biostudies-literature